若实数X,Y满足X√1-X=√Y-2+√X-1,求(3X^2+XY-Y^2)/(X^2-XY+Y^2)的值

问题描述:

若实数X,Y满足X√1-X=√Y-2+√X-1,求(3X^2+XY-Y^2)/(X^2-XY+Y^2)的值
SOS.

X√1-X=√Y-2+√X-1
1-X>=0
X-1>=0
所以x=1
代入,0=√Y-2+0
所以Y=2
(3X^2+XY-Y^2)/(X^2-XY+Y^2)
=(3×1^2+1×2-2^2)/(1^2-1×2+2^2)
=1/3